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Stocks rallied Friday after the release of a surprisingly strong monthly jobs report.

The U.S. economy added a better-than-expected 204,000 jobs in October despite a federal government shutdown that was expected to limit payroll growth. Despite the gains, the unemployment rate edged up to 7.3% from 7.2%.

The Dow Jones industrial average rose 167.80 points, or 1.1%, to hit a record close of 15,761.78, according to preliminary calculations. That topped the previous record close of 15,746.88 on Wednesday.

The Standard & Poor's 500 index gained 23.46, or 1.3%, to 1,770.61, just shy of its record close of 1,771.95. The Nasdaq composite index surged 61.90 points, or 1.6%, to 3,919.23.

In the prior session, the Dow fell 0.1% to 15,727 while the broader S&P 500 shed 0.4% to 1,764. The Nasdaq composite plummeted 1.9% to 3,857.33.

Twitter pulled back in its second day of trading and shares fell $3.25, or 7.2%, to $41.65. On Thursday, Twitter shares (TWTR) debuted and ended the day 73% above the offering price at $44.90.

Stock gains were led by banks, such as Bank of America and JPMorgan, which stand to benefit from a pickup in lending as the economy strengthens. Shares of JPMorgan Chase rose 4.5% to $53.96 and Bank of America gained 3.8% to $14.32. Goldman Sachs rose 2.2% to $163.17.

The jobs survey left investors grappling with how to interpret this week's surprisingly strong economic data and what it means for the Federal Reserve's economic stimulus program. On Thursday the government reported that U.S. economic growth accelerated in the third quarter. The Fed's stimulus has helped power this year's stock rally.

"We're walking a tight wire with the Fed," said Rob Lutts, Chief Investment Officer at Cabot Money Management. Lutts said the job survey was positive because it showed the economy was improving, but perhaps not strongly enough to assure that Fed policymakers will pull back on its bond-buying program before the end of year.

The reaction to the jobs report was more notable in the bond market than in the stock market. The yield on the 10-year Treasury note jumped to its highest level in six weeks as investors sold bonds.

The yield on the 10-year note jumped to 2.75% from 2.60% on Thursday, its highest level since Sept. 20.

The Fed has been buying $85 billion worth of bonds each month since December in an effort to keep interest rates low and boost the economy. Due to the design of the program, the Fed's actions have had a secondary effect of driving up stock prices by making bonds look expensive by comparison.

Asian stocks on Friday followed Wall Street's Thursday drop after the release of quarterly U.S. economic data showed the economy grew 2.8% in the third quarter, nearly a percentage point faster than economists had predicted.

Investors in Asia were also hanging back on Friday ahead of a weekend meeting in Beijing where China's communist leaders are expected to lay out their long-term plan for the world's No. 2 economy. A report that showed strong growth in Chinese exports last month was not enough to counter investor caution.

European shares were digesting a cut to France's credit rating by the Standard & Poor's ratings firm by one notch to AA. In a statement Friday, the rating agency said it feared the French government will struggle to reduce its deficit and debt and make the necessary reforms to make its economy more competitive. France's CAC 40 index fell 0.5% to 4,260.44.